Finite Group Databasebeta

← #28390534

Subgroups — #28390534

Order 14464.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813669C211yesmaximal, characteristic
2C2×#16813550C211yesmaximal, characteristic, complemented
3#20298600C211yesmaximal, characteristic, complemented
4#20298599C211yesmaximal, characteristic, complemented
5C2×#16813540C211yesmaximal, characteristic, complemented
6#20298504C211yesmaximal, characteristic, complemented
7C2×#104×C113C211yesmaximal, characteristic, complemented
8#16813669—22no—
9#16813669—22no—
10#16813669—22no—
11#16813669C414yescomplemented
12C2×#14268647—21no—
13C2×#14268647C2211yescharacteristic
14C2×#14268646—22no—
15C2×#14268646—21no—
16C22×Dic226—21no—
17C22×Dic226C2211yescharacteristic
18C2×Q8×D113—21no—
19C2×#14268631C2211yescharacteristic
20C2×C4⋊Dic113C2211yescharacteristic
21#16813550—22no—
22#16813547—21no—
23#16813546—21no—
24#16813544—21no—
25#16813543—21no—
26#16813540—22no—
27#16813529—22no—
28C2×#41×C113C2211yescharacteristic
29C2×M16×C113C2211yescharacteristic
30C2×C42×C113C2211yescharacteristic
31#104×C113—22no—
32#14268647—24no—
33#14268647—21no—
34#14268647—21no—
35#14268647—24no—
36#14268647C2×C412yes—
37#14268647D412yes—
38#14268646—28no—
39#14268646—24no—
40#14268646—24no—
41#14268646—28no—
42C2×Dic226—22no—
43C2×Dic226—24no—
44C2×Dic226—21no—
45C2×Dic226—21no—
46C2×Dic226—21no—
47C2×Dic226—21no—
48C2×Dic226—24no—
49C2×Dic226C2×C412yes—
50C2×Dic226D412yes—
51C2×Dic226D411yescharacteristic
52Q8×D113—24no—
53Q8×D113—24no—
54C2×D452D411yescharacteristic
55C2×C22⋊D113—22no—
56C2×C22⋊D113—21no—
57C22×Dic113—22no—
58C22×Dic113—21no—
59C22×Dic113D412yes—
60C2×C4×D113—22no—
61C2×C4×D113—21no—
62#14268631—21no—
63#14268631—21no—
64C2×#11744751—21no—
65C4⋊Dic113—21no—
66C4⋊Dic113—21no—
67#41×C113—21no—
68#41×C113—21no—
69#41×C113C2×C412yes—
70#41×C113D412yes—
71C2×Q8×C113D411yescharacteristic
72C2×D4×C113—21no—
73C2×D4×C113D411yescharacteristic
74C22×C4×C113—21no—
75C22×C4×C113—21no—
76C22×C4×C113C2311yescharacteristic
77M16×C113—21no—
78M16×C113—21no—
79C2×C8×C113—21no—
80C42×C113—21no—
81C42×C113—21no—
82C23×C113—21no—
83C23×C113C2×D411yescharacteristic
84C22×D113—21no—
85Q8×C113—21no—
86Q8×C113C22⋊C412yes—
87D4×C113—22no—
88D4×C113—22no—
89D4×C113—21no—
90D4×C113C22⋊C412yes—
91C2×C4×C113—21no—
92C2×C4×C113—22no—
93C2×C4×C113—22no—
94C2×C4×C113—22no—
95C2×C4×C113—41no—
96C2×C4×C113—41no—
97C2×C4×C113C22×C411yescharacteristic
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2×D411yescharacteristic
101C2×C4×C113C2×D411yescharacteristic
102C2×C4×C113C2×D411yescharacteristic
103C22⋊D113—28no—
104C22⋊D113—22no—
105C22⋊D113—22no—
106C2×Dic113—28no—
107C2×Dic113—21no—
108C2×Dic113—22no—
109C2×Dic113—22no—
110C2×Dic113—42no—
111C2×Dic113—41no—
112C2×Dic113C22⋊C414yes—
113D452—21no—
114D452C22⋊C412yes—
115C4×D113—28no—
116C4×D113—22no—
117C4×D113—22no—
118Dic226—28no—
119Dic226—22no—
120Dic226—22no—
121Dic226—22no—
122Dic226—22no—
123Dic226—21no—
124Dic226C22⋊C412yes—
125C8×C113—41no—
126#11744751—41no—
127C22×C113—21no—
128C22×C113—21no—
129C22×C113—22no—
130C22×C113—41no—
131C22×C113—41no—
132C22×C113C2×C22⋊C411yescharacteristic
133C22×C113#12011yescharacteristic
134C22×C113#12011yescharacteristic
135C2×D113—22no—
136C2×D113—41no—
137C2×D113—41no—
138C4×C113—22no—
139C4×C113—42no—
140C4×C113C2×C22⋊C411yescharacteristic
141C4×C113C2×C22⋊C411yescharacteristic
142C4×C113#12011yescharacteristic
143C4×C113#12011yescharacteristic
144Dic113—24no—
145Dic113—22no—
146Dic113—81no—
147C2×C113—21no—
148C2×C113—21no—
149C2×C113—42no—
150C2×C113#37911yescharacteristic
151C2×C113#45411yescharacteristic
152C2×C113#45611yescharacteristic
153D113—42no—
154#1793—1131nomaximal, Sylow
155C113#179311yescharacteristic, complemented, Sylow
156C2×2−1+4—1131no—
157C2×#104—1131no—
158C2×#104D11311yescharacteristic, complemented
159#417—1131no—
160#417—1131no—
161C2×#101—1131no—
162#391—1131no—
1632−1+4—1134no—
1642−1+4—2262no—
1652−1+4—2262no—
1662−1+4—2262no—
167C2×#41—1131no—
168C2×#41—2261no—
169C2×#41—2262no—
170C2×#41—2261no—
171C2×#41C2×D11311yescharacteristic
172C22×Q8—1131no—
173C22×Q8—2261no—
174C22×Q8—2261no—
175C2×M16—1131no—
176C2×M16C2×D11311yescharacteristic
177C2×C4⋊C4—1131no—
178C2×C42C2×D11311yescharacteristic
179#104—22no—
180#104—2262no—
181#103—2261no—
182#103—2261no—
183#102—2261no—
184#102—2261no—
185#101—2262no—
186#95—2262no—
187#41—21no—
188#41—21no—
189#41—1132no—
190#41—1132no—
191#41—2264no—
192#41—2264no—
193#41—2268no—
194#41—2268no—
195#41—2264no—
196#41—2264no—
197#41—2261no—
198#41—2261no—
199#41C4×D11312yes—
200#41C22⋊D11312yes—
201C2×Q8—1132no—
202C2×Q8—1132no—
203C2×Q8—1131no—
204C2×Q8—2264no—
205C2×Q8—2262no—
206C2×Q8—2264no—
207C2×Q8—2264no—
208C2×Q8—2264no—
209C2×Q8—2261no—
210C2×Q8—2261no—
211C2×Q8—2261no—
212C2×Q8—2261no—
213C2×Q8D45211yescharacteristic
214C2×D4—21no—
215C2×D4—1131no—
216C2×D4—2262no—
217C2×D4—2261no—
218C2×D4D45211yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—1132no—
222C22×C4—2262no—
223C22×C4—2261no—
224C22×C4—2262no—
225C22×C4—2261no—
226C22×C4C22×D11311yescharacteristic
227M16—21no—
228M16—21no—
229M16—2261no—
230M16—2261no—
231C2×C8—21no—
232C2×C8—2261no—
233C4⋊C4—2261no—
234C4⋊C4—2261no—
235C42—21no—
236C42—21no—
237C23—21no—
238C23—2261no—
239C23D4×D11311yescharacteristic
240Q8—21no—
241Q8—1132no—
242Q8—2268no—
243Q8—2262no—
244Q8—2262no—
245Q8—2262no—
246Q8—2261no—
247Q8—2262no—
248Q8#1426862412yes—
249D4—22no—
250D4—22no—
251D4—21no—
252D4—1132no—
253D4—2268no—
254D4—2262no—
255D4—2262no—
256D4—2261no—
257D4#1426862412yes—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—1134no—
265C2×C4—4522no—
266C2×C4—4521no—
267C2×C4—2268no—
268C2×C4—2268no—
269C2×C4—2262no—
270C2×C4—2262no—
271C2×C4—2261no—
272C2×C4—2262no—
273C2×C4—2262no—
274C2×C4C2×C4×D11311yescharacteristic
275C2×C4D4×D11311yescharacteristic
276C2×C4D4×D11311yescharacteristic
277C2×C4D4×D11311yescharacteristic
278C2×C4C2×C22⋊D11311yescharacteristic
279C2×C4C2×D45211yescharacteristic
280C8—41no—
281C8—4521no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—4521no—
288C22—4521no—
289C22—2262no—
290C22C22⋊C4×D11311yescharacteristic
291C22#1681359011yescharacteristic
292C22#1681359211yescharacteristic
293C4—22no—
294C4—42no—
295C4—9041no—
296C4—2264no—
297C4—2262no—
298C4C22⋊C4×D11311yescharacteristic
299C4C2×#1426862411yescharacteristic
300C4#1681359011yescharacteristic
301C4#1681359211yescharacteristic
302C2—21no—
303C2—21no—
304C2—42no—
305C2—4522no—
306C2#2029845311yescharacteristic
307C2#2029877211yescharacteristic
308C2#2029878211yescharacteristic
subgroupG/H
centerC22#16813592
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×#104×C113C2
socleC22×C113#120
prime radicalC2×#16813669C2
cosocleC22×C4×C113C23
hypercenterC2×#104D113
hypocenterC113#1793
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16813550C2semidirect
3. #20298600C2semidirect
4. #20298599C2semidirect
5. C2×#16813540C2semidirect
6. #20298504C2semidirect
7. C2×#104×C113C2semidirect
11. #16813669C4semidirect
155. C113#1793semidirect
158. C2×#104D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168136692
C2×#168135502
#202986002
#202985992
C2×#168135402
#202985042
C2×#104×C1132
#1793113